Abstract
The paper is devoted to the formulation and solution of the boundary value problem for a hollow circular cylinder whose properties continuously depend on the radial coordinate. It is shown that the mathematical model of such a problem is a homogeneous second-order differential equation with variable coefficients and two boundary conditions. In the case where the Poisson's ratio is constant and the Young's modulus logarithmically depends on the radial coordinate, the resulting equation can be reduced to the Whittaker equation, the solution of which is a linear combination of confluent hypergeometric functions. Based on this, an analytical solution of the boundary value problem is constructed in this particular case. Functions describing displacements, strains, and stresses occurring in the cylinder are found.
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